Although the NMSE will converge to zero with infinite \(N\) , Corollary REF  shows that different from increasing \(\tau \) , the MSE under LMMSE estimator will converge to a non-zero constant. It is interesting to find that the asymptotic MSE in (REF ) is the same as the MSE performance of least-squares (LS) estimator[1]}. It is well-known that the LS estimator has a worse estimation quality than the LMMSE estimator. Therefore, we can roughly deduce that the MSE performance under LMMSE is an increasing function of \(N\)  which converges to an upper bound of the LS estimator. This result will be validated in Section .
